Methods for compressing and decompressing data representing a digital three-dimensional object and information-recording medium for recording information containing said data

ABSTRACT

A compression method includes simplifying a mesh that represents a textured 3D-object by replacing polygons in the mesh with new ones that have broader faces. The method includes identifying adjacent polygons with different textures and adding vertices at the same positions as two vertices in the polygons. This creates two new edges and an intermediate polygon interposed between the two adjacent polygons. The new edges have zero length and the new polygon has zero area.

RELATED APPLICATIONS

This application is the national stage of international applicationPCT/FR2015/053122, filed on Nov. 18, 2015, which claims the benefit ofthe Nov. 21, 2014 priority date of French application FR1461318, thecontents of which are herein incorporated by reference.

FIELD OF INVENTION

The invention concerns data compression, and in particular, compressionand decompression of data representative of a three-dimensional object.

BACKGROUND

Typically, in the field of computer vision and three-dimensionalcomputer graphics, a three-dimensional object is represented digitallyin the form of a polygonal mesh. This mesh is formed from a plurality ofplanar polygons which are contiguous with each other. Each polygoncomprises a plurality of vertices interconnected by edges which delimitone face of the polygon.

Progressive compression methods facilitate transmission of athree-dimensional object from a server of multimedia content to a clientterminal on which the object needs to be displayed. In these methods,the mesh is gradually simplified by decimating vertices in order. Thisreduces the mesh size. The simplified mesh is transmitted to theterminal, where it is displayed. It is then gradually reconstructed onthis terminal from incremental data transmitted afterwards until thethree-dimensional object such as it was initially prior to thecompression is recovered.

Certain three-dimensional objects are textured. This means that thepolygons of the mesh have their surface covered by a digital image,known as a “texture.”

Difficulties arise when the object is textured. In such cases, duringthe progressive displaying of the three-dimensional object in the courseof the decompression, these methods can generate graphic artifacts.

SUMMARY

The invention provides a method of progressive compression of athree-dimensional object that limits the appearance of such graphicartifacts on the object when it contains textures.

In data compression, a problem occurs when a three-dimensional objectcontains polygons adjacent to each other and whose textures aredifferent. The problem occurs in particular in the area of bordersbetween portions of the object having very different textures from eachother.

One compression method selects the vertices to be eliminated as afunction of geometrical properties of the mesh, without consideringtexture information of the polygons. Thus, the common edge separatingthese adjacent polygons may be eliminated on account of thesimplification. The information concerning the fact that, prior tosimplification of the mesh, different textures existed on either side ofthe edge so eliminated, is thus absent from the resulting simplifiedmesh. Hence, during the decompression, when this simplified mesh isdisplayed, a graphic artifact will appear. This degrades the visualquality of the three-dimensional object perceived during itsdecompression.

In the above method, the finding of first and second polygons makes itpossible to identify the polygons where an artifact is liable to appearif the simplification were done directly. The replacement, in the secondpolygon, of the first and second shared vertices by third and fourthdistinct vertices and the creation of the edges makes it possible toseparate the first and second polygons. They are thus no longer adjacentto each other. Hence, for example, the deletion of the first or thesecond vertex does not entail as a consequence the disappearance of thefirst and second polygons at the same time. During the compression, theinformation concerning the texture difference is thus preserved at leastinsofar as the first, second, third and fourth vertices have not beendeleted from the simplified mesh. This information is thus preservedlonger during the compression process. Therefore, on the other hand,during the decompression this information will reappear much earlier inthe simplified mesh displayed on the screen. One thus minimizes the timeduring which such an artifact is visible, which improves the visualquality of the object displayed in the course of the decompression.

Finally, since the third and fourth vertices occupy the same position asthe first and second vertices and the length of the edges is zero, theouter appearance of the object has not been modified by this creation ofsupplemental vertices.

According to another aspect, the invention further concerns a set ofcompressed data representative of a three-dimensional digital object.

According to another aspect, the invention further concerns aninformation recording medium containing the set of data representativeof a three-dimensional digital object compressed according to theinvention.

According to another aspect, the invention further concerns a method ofdecompressing data representative of a three-dimensional digital object.

According to another aspect, the invention further concerns a method oftransmission of data representative of a three-dimensional digitalobject between a transmitter and a receiver, the method involving: thecompression of the data acquired by means of a compression methodaccording to the invention; and the decompression, by the receiver, ofthe compressed data so transferred, by means of a decompression methodaccording to the invention.

The embodiments of the invention may have one or more of thecharacteristics of the dependent claims.

According to another aspect, the invention further concerns a tangibleand non-transitory information recording medium containing instructionsfor executing a method according to the invention when theseinstructions are executed by an electronic calculator.

According to another aspect, the invention finally concerns anelectronic calculator to carry out the foregoing compression methodand/or decompression method.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood upon perusal of the followingdescription, given solely as a nonlimiting example, and referring to thedrawings, in which:

FIG. 1 is a schematic illustration of a three-dimensional digitalobject;

FIG. 2 is a schematic illustration of a set of data representing aportion of the object shown in FIG. 1;

FIG. 3 is an illustration of a device for transmitting the data shown inFIG. 2;

FIG. 4 is a flow chart of a method of compressing of the data shown inFIG. 2;

FIG. 5 is a schematic illustration of a portion of the object shown inFIG. 2 as has been modified as a result of a step of the method of FIG.4;

FIGS. 6A to 6C are schematic illustrations of portions of the mesh ofthe object shown in FIG. 1 as modified during the execution of a step ofthe method of FIG. 4;

FIGS. 7A and 7B are schematic illustrations of the object shown in FIG.1 after application of the method of compression of FIG. 4;

FIGS. 8A and 8B are schematic illustrations of the object shown in FIG.1 after application of the method of compression of FIG. 4 when a stepof duplication of vertices is omitted from this method;

FIG. 9 is a schematic illustration of an information recording mediumcontaining a set of data representative of the three-dimensional digitalobject compressed as a result of the method of FIG. 4;

FIG. 10 is a flow chart of a method of decompression of the objects ofFIGS. 7A to 8B in order to reconstruct the object of FIG. 1; and

FIG. 11 is a schematic illustration of another embodiment of a step ofthe method of FIG. 4.

In these figures, the same references are used to denote the sameelements.

In the following description, the characteristics and functions whichare well known to the skilled person shall not be described in detail.

DETAILED DESCRIPTION

FIG. 1 shows a three-dimensional original object 2, which in thisexample is a frog. A checkerboard texture has been applied to theoriginal object 2. This original object 2 comprises a mesh 4 and atexture atlas 6. The texture atlas 6 presents a black-and-whitecheckerboard pattern that covers the entire outer surface of the mesh 4.

Planar polygons contiguous with each other form the polygonal mesh 4.Each polygon comprises vertices, edges joining the vertices of thepolygon two-by-two, and a face bounded by the edges. In the examplesshown herein, the mesh 4 contains no hole.

The texture atlas 6 comprises a plurality of individual textures, eachof which covers a face of a polygon in the mesh 4. Each texture is atwo-dimensional image. In some embodiments, the image is a raster image.The technique illustrated herein is referred to as “texture mapping.”

In the illustrated embodiments, the polygons are triangular. In fact,most graphical processing units are optimized for processing triangularpolygons. Thus, throughout this description, the terms “triangle” and“polygon” are interchangeable unless otherwise indicated.

FIG. 2 shows a digital data-set 10 that is used to represent theoriginal object 2. In one example, the data set 10 is compatible withthe standard “OpenGL” (open graphics library).

For simplicity, only first and second triangles 12, 14 of the mesh 4 asstored in the data-set 10 will be described herein. The first and secondtriangles 12, 14 can be seen in FIG. 2.

Throughout this description, the original object 2 and the data set 10representative of the original object 2 shall be referred tointerchangeably. Thus, “acquisition of the original object 2” means“acquisition of the data set 10 that represents that original object 2.”

The data set 10 comprises the texture atlas 6, a vertex list 22, whichlists the vertices of the polygons of the mesh 4, a polygon list 24,which lists the polygons of the mesh 4; and a texture list 26, whichlists texture coordinates of the polygons of the mesh 4.

The texture atlas 6 contains all the textures needed to fill in eachface of each polygon of the mesh 4. Each texture of a face of a polygonis indexed within the texture atlas 6 by a set of three UV coordinates(Ua, Va), (Ub, Vb), and (Uc, Vc).

For example, when the texture atlas 6 contains a two-dimensional rasterimage 27, as shown in FIG. 2, UV coordinates, (Ua, Va), (Ub, Vb), and(Uc, Vc), code the positions of three points in an orthonormalizedreference system of the image 27. These three points delimit a “texturepiece” of the image 27. It is this texture piece that fills in the faceof a polygon.

Each texture piece has the same shape as the polygon to which itcorresponds. Thus, each texture piece has a triangular shape that hasexactly the same dimensions as the face of the polygon that it isintended to fill. However, the vertices of the texture pieces are notvertices of the mesh 4. To avoid any confusion, the term “point” shalldesignate a vertex of a texture piece.

The first and second polygons 12, 14 have corresponding first and secondtexture pieces 28, 29 in the image 27. The first texture piece 28 has UVcoordinates (U1 a, V1 a), (U1 b, V1 b), and (U1 c, V1 c). The secondtexture piece 29 has UV coordinates (U2 a, V2 a), (U2 b, V2 b), and (U2c, V2 c).

Typically, the texture atlas 6 is organized such that the texturespresenting different graphical properties are put in distinct locationsof the image 27. An example of a graphical property would be a valuerepresentative of pixel intensities.

The vertex list 22 contains, for each vertex, the coordinates of thatvertex as expressed in a reference system in space. In the example shownin FIG. 2, A, B, and C are vertices of the polygon 12. The secondpolygon 14 comprises the vertices B, C, and D since, in this example,the first and second polygons 12, 14 are adjacent and the vertices B andC are shared by the first and second polygons 12, 14.

The polygon list 24 contains, for each polygon, an entry enumeratingthose vertices from the vertex list 22 that are contained in thispolygon. For example, the entry for the polygon 12 in the polygon list24, denoted “P1,” contains the vertices “ABC”.

The texture list 26 contains, for each polygon of the polygon list 24, aset of UV coordinates defining the texture piece associated with thispolygon. For example, the entry “P1” associated with the first polygon12 contains the coordinates, denoted (u1, v1), of the three points thatdelimit the first texture piece 28 in the texture atlas 6. The same goesfor the entry, denoted P2, corresponding to the second polygon 14. Theentry P2 is associated, by the texture list 26, with the coordinates(u2, v2) of the three points that delimit the texture piece 29.

FIG. 3 shows an example of a device for transmitting the original object2 from a transmitter 40 to a receiver 42. The transmitter 40 and thereceiver 42 exchange data between them using a data-exchange link 44.Generally, the transmitter 40 and the receiver 42 are separated fromeach other by several meters or several kilometers. The data-exchangelink 44 is typically a link established by means of a long-distanceinformation transmission network such as the Internet (World Wide Web).

The transmitter 40 comprises a transmitter calculation-unit 46 thatincludes an information-recording medium 48, a programmable electroniccalculator 50, and a data-exchange interface 52.

The information-recording medium 48 contains the instructions needed toexecute the compression method described in connection with FIG. 4. Theelectronic calculator 50 reads and executes the instructions recorded onthe information-recording medium 48. The data-exchange interface 52enables the data set 10 to be exchanged and transferred on thedata-exchange link 44.

In some embodiments, the transmitter 40 is a multimediacontent-distribution server. In such embodiments, the receiver 42 is aclient terminal, such as a computer or a mobile communication device. Inparticular, the receiver 42 is capable of displaying, or rendering, theoriginal object 2. To accomplish this, the receiver 42 comprises agraphical processor 48 and a receiver calculation-unit 47 that issimilar to the transmitter calculation-unit 46.

The transmitter 40 compresses the data set 10 and sends it to thereceiver 42, which then decompresses it and renders the original object2 on a screen 49.

One example of compression of the data set 10 shall be described atfirst referring to the flow chart in FIG. 4 and with the aid of FIGS. 1to 7C. This method is a method of progressive compression of the mesh.

During a first step 60, the transmitter calculation-unit 46 acquires thedata set 10.

Then, in a second step 62, the mesh 4 is formatted for the followingsteps of the compression method. These steps, and especially thesimplification, will be described in more detail in the following.

The second step 62 involves, first of all, a finding operation 64 duringwhich first and second adjacent polygons having different textures arefound among the polygons of the mesh 4.

Two textures are said to be different if the intersection ofcorresponding texture pieces in the texture atlas 6 is a zero set, thatis, the texture pieces are completely separated in the texture atlas 6.For example, the first and second texture pieces 28, 29 are separatedsince the shortest distance between them is non-zero.

Two polygons are said to be adjacent if they have, between them, a firstand second shared vertex and if they are joined together by a sharededge.

In the illustrated embodiment, the first and second polygons 12, 14 areadjacent because they have shared vertices B, C that define a commonedge. Moreover, their respective first and second texture pieces 28, 29are different. As used herein, references to polygons 12, 14 shall beassumed to be references to adjacent polygons, and references to sharedvertices B, C shall be assumed to refer to the shared vertices of thosepolygons 12, 14.

In the embodiment described herein, the first and second polygons 12, 14are identified by automatic searching, with the aid of the polygon list24 and the texture list 26, for polygons that are both adjacent to eachother and also associated, by the texture list 26, with separate texturepieces.

Once such polygons 12, 14 have been identified, the second step 62involves, for each pair of polygons so identified, separating thosepolygons.

The process of separating polygons begins with a vertex-splittingoperation 66 during which the vertices B and C are replaced, in thepolygon 14, with vertices B′ and C′. The vertices B′ and C′ are known as“split vertices.” The vertices B′ and C′ occupy respectively the samepositions in space as the vertices B and C. Thus, they have the samecoordinates as the vertices B and C.

In some practices, the split vertices B′ and C′ are created in thevertex list 22 and the definition BCD of the polynomial 14 in thepolygon list 24 is replaced with the definition B′C′D. As a result, anew edge B′ C′ is created in the data set 10 and the edges BD and CD ofthe polygon 14 are replaced with these new edges B′D and C′D,respectively. This results in a modified polygon 14′, as shown in FIG.5. In this description, an edge that directly joins two vertices X and Yin a polygon shall have the reference “XY.”

During an edging operation 68, at least two edges of zero length arecreated: a first edge between the vertices B and B′ and a second edgebetween the vertices C and C′. This creates at least one intermediatepolygon interposed between the polygons 12 and 14′. These edges BB′ andCC′ join together the polygons 12, 14′. This connection is necessary inorder to avoid the appearance of a supplemental artifact at the junctionof the polygons 12, 14′, such as the appearance of a hole. The face ofthis intermediate polygon has a zero surface. This means that it is notvisible on a screen, and that it therefore creates no visible artifact.As shown in FIG. 5, since the polygons of the mesh 4 are necessarilytriangles, there are two intermediate triangles 67, 69 interposedbetween the polygons 12 and 14′ that are created. For example, asupplemental edge B′C is created to form the first and secondintermediate triangles 67, 69. The first intermediate triangle 67 isdelimited by the edges BC, CB′ and BB′ and the second intermediatetriangle 69 is delimited by the edges B′C′, CC′ and CB′. The new edgesBB′, CC′, and CB′ are created by adding the definitions of the first andsecond intermediate triangles 67, 69 to the polygon list 24. The firstand second intermediate triangles 67, 69 have a texture value of zero.As a result, the texture list 26 does not match them to any texturepiece.

To facilitate an understanding of FIG. 5, the first and secondintermediate triangles 67, 69 are drawn with a non-zero surface faceeven though, as explained above, they have a zero surface. Likewise, inFIG. 5, the edges BB′, CC′ are represented with a nonzero length eventhough, as explained above, this is not the case. The fact that apolygon has a face with zero area does not mean it does not exist in themesh 4, since every polygon there is defined as a function of itsvertices in the polygon list 24. The same is true of the edges.

The vertex-splitting operation 66 and the edging operation 68 come downto a corresponding modification of the vertex list, 22, the polygon list24, and the texture list 26 of the data set 10 to reflect themodifications to the mesh 4.

The duplication of the vertices B and C, and their replacement n thepolygon 14 with the vertices B′ and C′, makes it possible to separatethe polygons 12, 14 from each other. This prevents losing theinformation that a texture difference exists between these two polygonswhen one of the vertices B and C is deleted. Moreover, the fact that thevertices B′ and C′ are joined to the vertices B and C by edges preventsthe polygons 12, 14′ from being displaced relative to each other duringthe rest of the method. Such a displacement would create holes in themesh 4, which would degrade the graphical quality of the original object2. The zero value of the lengths of the edges and of the surface of theface of the polygons 67, 69 mean that this duplication of the vertices Band C does not entail a modification of the exterior graphicalappearance of the mesh 4 and thus of the original object 2. These edgesmake possible a local modification of the connectivity of the mesh 4, sothat further simplification operations that are based on connectivityinformation do not result in too rapid a disappearance of thesepolygons.

When no other pair of adjacent polygons with different texture is foundin the modified data set 10, the second step 62 finishes. Once thesecond step 62 finishes, the mesh 4 has no adjacent polygons ofdifferent texture.

A third step 70 simplifies the mesh 4. This simplification involvesdeleting vertices, and thus polygons, from the mesh 4. The purpose ofthis simplification is to create new polygons having a broader face thanthe deleted polygons. These new polygons will replace the deletedpolygons. The resulting simplified image thus takes up less space inmemory.

The third step 70 includes an identification operation 72, a deletionoperation 74, and a creation operation 76.

The identification operation 72 identifies, as a function of apredetermined criterion, vertices to be deleted. Although a variety ofways are available for executing the identification operation 72, asuitable way to do so is to select the vertices from the vertex list 22on the basis of connectivity criteria, such as the number of theirclosest neighbors.

The deletion operation 74 deletes the vertices thus identified and theedges joining these vertices to each other and to other vertices of themesh 4. The deletion operation 74 thus results in deleting polygons fromthe mesh 4.

The creation operation 76 creates new edges and new textures. The newedges join the vertices that have not been deleted, thus creating thenew polygons. The new textures cover the faces of the new polygons fromthe respective textures of the deleted polygons.

Known methods for executing the third step 70 are described in“Rate-distortion optimization for progressive compression of 3D meshwith color attributes”, Ho Lee et al., The Visual Computer, vol. 28, p.137-153; Springer Verlag, May 2011, DOI: 10.1007/s00371-011-0602-y andP. Alliez et al. “Progressive compression for lossless transmission oftriangle meshes”, ACM Proceedings of SIGGRAPH, p. 195-202, 2001, thecontents of which are herein incorporated by reference.

FIGS. 6A to 6C illustrate the functioning of this algorithm on a portion80 of the mesh 4.

This algorithm functions in two steps: a conquest phase and a clean-upphase.

The identification operation 72 and the deletion operation 74 arecarried out during a conquest phase. During this phase, the algorithmtraverses the vertices of the mesh 4 automatically, step by step. Thisinvolves moving along the edges of the mesh 4 in the fashion of a graph.A predefined “graph traversal” defines the order in which the algorithmtraverses the vertices.

For each vertex encountered during traversal, the algorithm determines a“valence” of that vertex. The “valence” of a vertex is the number ofimmediate neighbors S′ of that vertex to which it is directly connectedby edges. If a vertex S has a valence less than a predeterminedthreshold, the algorithm deletes both that vertex and the edges SS′joining it its immediate neighbors. These edges SS′ can be seen in FIG.6A. The algorithm then creates new edges 80, 81, 82 that are to replacethe deleted edges SS'. These new edges can be seen in FIG. 6B.

In the clean-up phase, the algorithm advantageously deletes certainexcess vertices 83 as well as the edges joining those vertices. It thencreates new edges as replacements. This results in new polygons 84having a regular form. The creation operation 76 creates these new edgesduring the clean-up phase.

The identification operation 72, the deletion operation 74, and thecreation operation 76 also modify of the vertex list 22, the polygonlist 24, the texture list 26, and the texture atlas 6 to reflect themodifications made to the mesh 4.

Advantageously, the third step 70 also includes a recording operation 89that records incremental, or refinement, data. This incremental dataindicates which vertices and the edges were deleted as well as whichvertices and edges were created during the third step 70.

In some practices, the incremental data contains a list of the verticesdeleted during the third step 70, as well as a list giving, for each ofthese deleted vertices, the set of neighboring vertices to which thisdeleted vertex was directly connected by an edge. The incremental data,when used as part of a decompression method, make it possible to performoperations that are the inverses of the operations performed during thethird step 70. This makes it possible to reconstruct the mesh 4 such asit existed prior to the application of the third step 70 from thesimplified mesh obtained at the end of the third step 70 and thisincremental data. In some practices, the incremental data also includesinformation making it possible to find the texture piece associated witheach reconstructed polygon without loss of information.

The third step 70 simplifies the original object 2 into a simplifiedobject 94 that has fewer vertices and polygons than the original object2. Because of this lower resolution, the data set required to representthe simplified object 94 is smaller than the data set 10 required torepresent the original object 2. This facilitates transmission of thesimplified object 94.

Some practices repeat the simplification several times in order toobtain a higher compression ratio. Referring to FIG. 4, such practicesinclude, at the end of the third step 70, a fourth step 91 foradditional simplification. In a typical practice, the fourth step 91 isidentical to the third step 70, except that it is performed on thesimplified object 94 in order to further simplify it. Typically, witheach iteration of the fourth step 91, the algorithm broadens theselection criteria for the vertices to be deleted, thereby ensuring thedeletion of additional vertices.

One thus obtains, at the end of the fourth step 91, a final object 96,as illustrated in FIG. 7B. The final object 96 contains even fewervertices and polygons than the simplified object 94 that precedes it.The final object 96 is thus an even more simplified version of theoriginal object 2 than the simplified object 94. The incremental datagenerated during this performance of the fourth step 91 is likewiserecorded as discussed in connection with the recording operation 89.

Referring back to FIG. 4, during a fifth step 92, the final object 96 istransmitted to the interface 50.

The present method is particularly advantageous for reducing theappearance of graphical artifacts in the simplified object 94 and in thefinal object 96 at the end of their compression.

Progressive compression methods ignore texture differences betweenadjacent polygons. As a result, the vertices B and C of the first andsecond polygons 12, 14 may be quickly deleted during the deletionoperation 74. The first and second polygons 12, 14 are then deleted andreplaced by new polygons. The texture of the polygons is then replacedby a new texture determined from the points of the first and secondtexture pieces 28, 29.

For example, it often happens that one of these new polygons ends upbeing associated with a new texture piece defined by two points of thesecond texture piece 29 and one point of the first texture piece 28.This new piece includes a portion of the image 27 located between thefirst and second texture pieces 28, 29. This portion is often completelydifferent from the first and second texture pieces 28, 29. This thencauses the appearance, at the location of the polygons 12, 14 in thesimplified object 94, of a texture piece that is very different and thusparticularly visible. This creates a graphical artifact that isparticularly conspicuous on account of the texture difference betweenthe first and second polygons 12, 14.

To illustrated the distinction, FIG. 8A illustrates another simplifiedobject 94′ that results from compression of the original object 2 butwith the second step 62 having been omitted. The procedure used isidentical to that shown in FIG. 4, but without the optional fourth step91. Similarly, FIG. 8B shows another final object 96′ that results fromhaving compressed the original object 2 using the third and fourth steps70, 91 but with the omission of the second step 62.

A comparison of the compressed FIGS. 7A and 7B with the compressed FIGS.8A and 8B shows the unmistakable benefit of the second step 62. As isapparent, a graphical artifact 100 present in FIG. 8A is nowhere to beseen in FIG. 7A. Similarly, a graphical artifact 102 present in FIG. 8Bis nowhere to be seen in FIG. 7B.

These artifacts 100, 102 arose directly as a result of omitting thesecond step 62. They correspond to polygons whose texture informationhas been lost in whole or in part during the third or fourth steps 70,91. This loss of information results from the deletion of adjacentpolygons having different textures. Since these polygons were notsubjected to a separation during the second step 62 prior to thesimplification step, they were deleted during the deletion operation 74.

In contrast, the method of FIG. 4 retains information indicating thatthe adjacent first and second polygons 12 and 14. This is because noneof the vertices B, B′, C, C′ have actually been deleted. Thisinformation may eventually be lost after enough iterations of the thirdand fourth steps 70, 91. However, in most practical cases, the proceduredescribed herein avoids these artifacts.

Now, as will be understood from perusal of the following, the later thestage of compression in which the visual artifact appears, the morequickly it disappears during the decompression. With the method of FIG.4, during the decompression the artifacts are thus deleted or are muchmore ephemeral.

FIG. 9 shows an information recording medium 104 containing a data set106 representative of the final object 96.

The simplified final object 96 is afterwards sent by the transmitter 40to the receiver 42, in order to be rendered there. Likewise, theincremental data respectively associated with each execution of thethird or fourth step 70, 91 is sent from the transmitter 40 to thereceiver 42. In some practices, this transmission is done sequentially.

FIG. 10 illustrates the decompression method to reconstruct the originalobject 2. An example of such a method is that described in French patentapplication FR2998685.

During an acquisition step 110, the receiver 42 acquires datarepresentative of the final object 96, the data having been sent fromthe transmitter 40. The receiver 42 then immediately renders the object96 so received.

Next, during a first reconstruction step 112, the receiver 42automatically reconstructs the simplified object 94 from the finalobject 96. It does so with the help of the incremental data that wasgenerated during the fourth step 91. To do so, the receiver 42 performsoperations that are inverses of those performed during the fourth step91.

The receiver 42 typically receives incremental data after it has alreadyreceived the data representing the final object 96. In some cases, thereceiver 42 receives this incremental data after having already renderedthe final object 96 on the screen 49.

From the incremental data, the receiver 42 modifies the final object 96.Such modification includes restoring those vertices of the mesh 4 thathad been deleted during the fourth step 91. In doing so, the receiver 42deletes of certain polygons of the mesh of the object 96 and replacesthem with substitute polygons that are more numerous and that have amore reduced surface area.

In particular, the receiver 42: adds, to the final object 96, thosevertices that were deleted during the simplification carried out duringthe fourth step 91. It then replaces those edges of the mesh that werecreated during the fourth step 91 with supplemental edges that join theadded vertices to the existing vertices of the object 96. This createssupplemental polygons. Finally, it creates supplemental texture piecesfor these supplemental polygons from the respective textures of thereplaced polygons and from the incremental data.

At the end of the first reconstruction step 112, the receiver 42 willhave reconstructed the simplified object 94. The receiver 42 thenrenders the simplified object 94 in place of the final object 96 on thescreen 49.

Then, during a second reconstruction step 114, the receiver 42reconstructs the original object 2 from the simplified object 94. Itdoes so with the aid of the incremental data that was generated duringthe third step 70. In some practices, the second reconstruction step 114is identical to the first reconstruction step 112, except that it isapplied to the simplified object 94 rather than to the final object 96.

The original object 2 is thus progressively reconstructed, by successiverefinements, from incremental data, with an increasing precision in thecourse of their reception, until reaching a level of detail identical orclose to that which it had prior to the compression. The intermediatesimplified objects, such as the simplified object 94, are rendered assoon as they are reconstructed. The receiver 42 thus renders objectswhose precision increases as it receives the incremental data andperforms the steps of reconstruction.

This method is useful when the flow rate of the data-exchange link 44 islimited or subject to major variations because it prevents the renderingof the object at the receiver 42 from being disturbed by a “lag” effect.This method also limits the waiting time for the object to be rendered(even in a simplified version) by the receiver 42, as compared to thecase in which it would be necessary to wait for the whole compressedoriginal object 2 to be sent to the receiver 42 before being able tostart the decompression and then the rendering.

Since the simplified objects are rendered during the decompression inthe inverse order of their creation by the compression, the later thevisual artifact appears during the compression the more quickly it willdisappear during the decompression and thus from the progressiverendering of the decompressed object.

Advantageously, during a formatting step 116, the mesh of thereconstructed original object 2 is formatted to delete the vertices andedges that were created during the second step 62. This formatting step116 involves replacing the vertices B′, C′ respectively with thevertices B, C and deleting the edges BB′, CC′, and B′ C.

Thus, the polygons 67, 69 are deleted and the polygons 12, 14 once againtake on their initial configuration in the original object 2.

Many other embodiments are possible.

The object 2 can be different. It may involve any object able to berepresented in the form of a mesh. Likewise, the texture atlas 6 can bechosen differently.

The polygons may be other than triangular. For example, the polygons maybe parallelograms.

In some embodiments, the data set 10 is recorded in a format compatiblewith a different graphical standard, such as Direct3D.

The transmitter 40 may be different. For example, the transmittercalculation-unit 46 may be distinct from the transmitter 40. In suchcases, the compression of the original object 2 is not done by thetransmitter 40. Instead, the transmitter's only role is that oftransferring the data to the receiver 42.

The receiver 42 may be different. For example, the receiver 42 may be atablet, a mobile telephone, or a television set. The rendering of theoriginal object 2 may likewise be done independently of the reception.The term “receiver” 42 thus encompasses two distinct devices, onereceiving the original object 2 and the other one rendering thisoriginal object 2.

The second step 62 may be performed in different ways.

In particular, the finding operation 64 can be performed differently inorder to identify adjacent polygons. For example, FIG. 11 illustratesanother method of identifying the polygons 12, 14 in a portion of themesh 4. By this method, the edges of the mesh are automaticallytraversed by selecting the vertices of the mesh one after another in apredetermined order. For each selected vertex 150, all of the vertices152, 153 immediately adjacent to this vertex 150 are traversed, movingabout the vertex 150 in a predefined direction, identified here by thearrow 154. These adjacent vertices are defined as being the verticesdirectly connected to the vertex 150 by an edge. For simplicity, onlythe vertices 152 and 153 are denoted by a reference number. One thendetermines vertices 152 and 153 having another immediately adjacentshared vertex 156 other than the vertex 150, if such exist. If so, thisindicates that the vertices 152, 153 are shared by several polygons. Inthis example, one identifies the adjacent polygons 158 and 160. Thepolygon 158 comprises the vertices 150, 152 and 153. The polygon 160comprises the vertices 152, 153 and 156. One then checks to make surethat the texture pieces associated with the polygons 158 and 160 aredifferent.

As a variant, it is the vertices B, C of the polygon 12 that arereplaced with the vertices B′, C′.

The fourth step 91 may be omitted. In this case, the object 94 is thefinal object that is transmitted. The first reconstruction step 112 isthen omitted from the decompression method.

Other practices of the method include repeating the fourth step 91several times. This increases the compression level of the originalobject 2 prior to its transmission. The decompression method thenincludes a number of steps identical to the first reconstruction step112, the number equaling the number of times that the fourth step 91 wasrepeated.

In another practice of the method, when the fourth step 91 is performedat least once, then the second step 62 is repeated, for example, priorto each performance of the fourth step 91. If the polygons 67, 69 weredeleted during a performance of the fourth step 91, they may thus berecreated before performing the fourth step 91 once more. This limitsthe risk of the polygons 12, 14 being deleted during the fourth step 91.In this case, the formatting step 116 may be repeated several times. Forexample, the formatting step 116 is applied during the decompressionafter the first reconstruction step 112 or after the secondreconstruction step 114.

Some practices of the method include performing the third step 70differently. An alternative way to execute the third step 70 is to usethe algorithm described in the following document: Maglo, A., Courbet,C., Alliez, P., “Progressive compression of manifold polygon meshes”,Computers and Graphics, 2012, DOI: 10. 1016/j.cag.2012.03.023.

Some practices omit the formatting step 116. Other practices carry outthe formatting step 116 after the first reconstruction step 112 to cleanup the mesh of the reconstructed object 94 before applying the secondreconstruction step 114.

In another practice, during the second step 62, the vertices B′, C′,just like the vertices B, C, are subject to marking during a fourthoperation 180, as shown in FIG. 4. This indicates that they shouldpreferably not be deleted during the third step 70. In such a practice,marking typically includes adding a predefined value of a supplementaldata bit added to the vertex list 22 for each vertex. Thus, during thethird step 70, a check is done during the identification operation 72 tosee if the vertex has such a marking.

For example, a first traversing of all the vertices of the mesh isperformed. If an unmarked vertex is found during this first traversal,and that unmarked vertex also meets the criteria for being deleted, thenit is deleted. On the other hand, if it has been marked, then it is notdeleted right away. Instead, it is identified in a specific list thatwill only be consulted during a second traversal of the mesh's vertices.

If the third step 70 can end without it being necessary to delete themarked vertex, then the marked vertex will not be deleted. Only if it isimpossible not to delete the marked vertex, for example, because itsdeletion is required in order to preserve certain properties ofregularity of the mesh, will it be deleted. In other words, the deletionof the marked vertex is delayed until absolutely necessary.

In some practices, vertex-marking repeats after each application of thethird and fourth steps 70, 91. This permits taking account ofmodifications of the mesh wrought by its simplification. In an extremecase, the deletion of a marked vertex is prohibited. This wouldguarantee that its deletion will not cause a visual artifact.

Other methods are possible to identify different texture pieces. In asimplified practice, texture pieces are different if they have no pointin common in the image 27. In another practice, texture pieces areconsidered to be different only if the minimum distance separating thetwo texture pieces exceeds a predetermined threshold. This predeterminedthreshold may be equal to zero or greater than zero.

Some practices of the method compare representative texturecharacteristics to decide whether texture pieces are different or not.For example, this characteristic is calculated for each texture pieceand then, if the offset between the value of this characteristic for afirst piece and a second piece is greater than a predeterminedthreshold, these texture pieces are said to be different. Examples ofsuitable characteristic include a median value, a maximum, or a minimumof a histogram of colors contained in the piece. In some practices ofthe method, the characteristic represents a quantity associated with thegraphical pattern appearing in the texture, such as a fractal dimensionor a Hurst exponent. The latter approach, which is based onrepresentative characteristics, does not rely on the positions of thepoints delimiting the texture pieces in the image 27.

Having described the invention, and a preferred embodiment thereof, whatwe claim as new, and secured by Letters Patent is: 1-11. (canceled) 12.A method comprising causing a computer system to carry out compressionof data representative of a three-dimensional object, said datacomprising a mesh that is formed by a plurality of planar polygons thatare contiguous with each other and a texture atlas that lists texturesof all polygons in said mesh, each polygon comprising vertices that arejoined by edges that delimit a face of said polygon and a texture thatcovers said face, wherein causing said computer system to carry outcompression of said data comprises causing said computer to acquire saiddata and causing said computer to carry out the act of simplifying saidmesh, wherein simplifying said mesh comprises deleting vertices fromsaid mesh, thereby deleting polygons and creating, in place of saiddeleted polygons, new polygons that have faces that are broader thanthose of said polygons that have been deleted, wherein deleting saidvertices from said mesh comprises identifying, as a function of apredetermined criterion, vertices to be deleted from said mesh, beforedeleting said identified vertices, identifying, in said mesh, first andsecond adjacent polygons that have different textures and that also havefirst and second shared vertices that are joined by a shared edge,providing a third vertex that occupies the same position in space assaid first shared vertex in said second polygon, providing a fourthvertex that occupies the same position in space as said second sharedvertex, creating a first edge between said first vertex and said thirdvertex, creating a second edge between said second vertex and saidfourth vertex, creating an intermediate polygon that is interposedbetween said first and second polygons, deleting said identifiedvertices and edges that join said identified vertices to other verticesof said mesh, thereby deleting polygons comprising said identifiedvertices and said edges, creating new edges to join vertices that havenot been deleted, thereby creating new polygons, and based at least inpart on textures of said deleted polygons, creating new textures forsaid new polygons, wherein two polygons are adjacent if said polygonshave a first shared vertex and a second shared vertex that are joinedtogether by a shared edge, wherein said first edge has zero length, andwherein said second edge and said first edge have the same length, andwherein said intermediate polygon has a surface area of zero.
 13. Themethod of claim 12, further comprising, prior to deleting said vertices,marking said first, second, third, and fourth vertices, whereinidentifying, as a function of a predetermined criterion, vertices to bedeleted from said mesh comprises identifying said first, second, third,and fourth vertices as meeting said predetermined criterion fordeletion, and wherein simplifying said mesh comprises refraining fromdeleting said first, second, third, and fourth vertices even though saidfirst, second, third, and fourth vertices have been found to meet saidpredetermined criterion.
 14. A manufacture comprising a non-transitorycomputer-readable medium having encoded thereon data representative of acompressed three-dimensional object, said data comprising a simplifiedmesh that has been formed from a plurality of polygons using the methodrecited in claim 12, and incremental decompression data, saidincremental decompression data comprising a list of vertices and edgesthat have been deleted from said mesh during said execution of saidcompression method, wherein at least one of said simplified mesh andsaid incremental decompression data encodes first, second, third, andfourth vertices of said mesh such that said first and third vertices arejoined together by an edge of zero length and said second and fourthvertices are joined together by an edge of zero length.
 15. A method ofdecompressing data representative of a compressed three-dimensionaldigital object, said method comprising acquiring data representative ofa compressed three-dimensional object as recited in claim 14,reconstructing a more complex mesh from said simplified mesh and saidincremental data, wherein reconstructing said more complex meshcomprises creating supplemental vertices in said simplified mesh fromsaid incremental data acquired and replacing edges of said simplifiedmesh with supplemental edges by joining said supplemental vertices toexisting vertices, thereby deleting polygons from said simplified meshand replacing said deleted polygons with supplemental polygons that havea smaller surface than said corresponding deleted polygons, creatingsupplemental textures for said supplemental polygons based at least inpart on respective textures of said polygons that has been replaced andsaid incremental data, wherein said more complex mesh comprises saidfirst and third vertices joined together by an edge of zero length andsaid second and fourth vertices joined together by an edge of zerolength.
 16. The method of claim 15, further comprising formatting saidreconstructed mesh, wherein formatting said reconstructed mesh comprisesreplacing said third and fourth vertices of said second polygon withsaid first and second vertex, respectively, and deleting said edges ofzero length between said first and third vertices and between saidsecond and fourth vertices.
 17. A method comprising causing transmissionof data representative of a three-dimensional digital object between atransmitter and a receiver, said method comprising, at said transmitter,acquiring data representative of said three-dimensional digital object,compressing said data using the method recited in claim 12, transferringsaid compressed data to said receiver through a data-exchange link, and,at said receiver, decompressing said compressed data, whereindecompressing said compressed data comprises reconstructing a morecomplex mesh from said simplified mesh and said incremental data,wherein reconstructing said more complex mesh comprises creatingsupplemental vertices in said simplified mesh from said incremental dataacquired and replacing edges of said simplified mesh with supplementaledges by joining said supplemental vertices to existing vertices,thereby deleting polygons from said simplified mesh and replacing saiddeleted polygons with supplemental polygons that have a smaller surfacethan said corresponding deleted polygons, creating supplemental texturesfor said supplemental polygons based at least in part on respectivetextures of said polygons that has been replaced and said incrementaldata, wherein said more complex mesh comprises said first and thirdvertices joined together by an edge of zero length and said second andfourth vertices joined together by an edge of zero length.
 18. Themethod of claim 12, further comprising determining that an intersectionof first and second textures is zero in said texture atlas, and, basedon said determination, determining that said first and second texturesdiffer
 19. The method of claim 12, further comprising determining ashortest distance that separates first and second textures in saidtexture atlas, determining that said shortest distance exceeds apredetermined threshold, based on said determination that that saidshortest distance exceeds a predetermined threshold, determining thatsaid first and second textures differ from each other.
 20. A manufacturecomprising a tangible and non-transitory computer-readable medium havingencoded thereon instructions for causing a computer to execute themethod recited in claim
 12. 21. An apparatus comprising a digitalinformation processing system configured to carry out the method recitedin claim 12.